(Non) Linear Regression Modeling

We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1, . . . , Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1, . . . ,Xp), p ∈ N, which explain or predict the dependent variables by means of the model. Such relationships and models are commonly referred to as regression models. --

(Non) Linear Regression Modeling

We will study causal relationships of a known form between random variables. Given a model, we distinguish one or more dependent (endogenous) variables Y = (Y1, . . . , Yl), l ∈ N, which are explained by a model, and independent (exogenous, explanatory) variables X = (X1, . . . ,Xp), p ∈ N, which explain or predict the dependent variables by means of the model. Such relationships and models are commonly referred to as regression models

Selection of tuning parameters in bridge regression models via Bayesian information criterion

We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning parameter in bridge regression models. The choice of the adjusted parameters can be viewed as a model selection and evaluation problem. We propose a model selection criterion for evaluating bridge regression models in terms of Bayesian approach. This selection criterion enables us to select the adjusted parameters objectively. We investigate the effectiveness of our proposed modeling strategy through some numerical examples.Comment: 20 pages, 5 figure

Efficient Scalable Accurate Regression Queries in In-DBMS Analytics

Recent trends aim to incorporate advanced data analytics capabilities within DBMSs. Linear regression queries are fundamental to exploratory analytics and predictive modeling. However, computing their exact answers leaves a lot to be desired in terms of efficiency and scalability. We contribute a novel predictive analytics model and associated regression query processing algorithms, which are efficient, scalable and accurate. We focus on predicting the answers to two key query types that reveal dependencies between the values of different attributes: (i) mean-value queries and (ii) multivariate linear regression queries, both within specific data subspaces defined based on the values of other attributes. Our algorithms achieve many orders of magnitude improvement in query processing efficiency and nearperfect approximations of the underlying relationships among data attributes

Bayesian Modeling and MCMC Computation in Linear Logistic Regression for Presence-only Data

Presence-only data are referred to situations in which, given a censoring mechanism, a binary response can be observed only with respect to on outcome, usually called \textit{presence}. In this work we present a Bayesian approach to the problem of presence-only data based on a two levels scheme. A probability law and a case-control design are combined to handle the double source of uncertainty: one due to the censoring and one due to the sampling. We propose a new formalization for the logistic model with presence-only data that allows further insight into inferential issues related to the model. We concentrate on the case of the linear logistic regression and, in order to make inference on the parameters of interest, we present a Markov Chain Monte Carlo algorithm with data augmentation that does not require the a priori knowledge of the population prevalence. A simulation study concerning 24,000 simulated datasets related to different scenarios is presented comparing our proposal to optimal benchmarks.Comment: Affiliations: Fabio Divino - Division of Physics, Computer Science and Mathematics, University of Molise Giovanna jona Lasinio and Natalia Golini - Department of Statistical Sciences, University of Rome "La Sapienza" Antti Penttinen - Department of Mathematics and Statistics, University of Jyv\"{a}skyl\"{a} CONTACT: [email protected], [email protected]

Alternating model trees

Model tree induction is a popular method for tackling regression problems requiring interpretable models. Model trees are decision trees with multiple linear regression models at the leaf nodes. In this paper, we propose a method for growing alternating model trees, a form of option tree for regression problems. The motivation is that alternating decision trees achieve high accuracy in classification problems because they represent an ensemble classifier as a single tree structure. As in alternating decision trees for classifi-cation, our alternating model trees for regression contain splitter and prediction nodes, but we use simple linear regression functions as opposed to constant predictors at the prediction nodes. Moreover, additive regression using forward stagewise modeling is applied to grow the tree rather than a boosting algorithm. The size of the tree is determined using cross-validation. Our empirical results show that alternating model trees achieve significantly lower squared error than standard model trees on several regression datasets